A contractor is building a new house. She creates a map with the coordinates A(6,12) , B(6,−6) , C(−4,−6) , and D(−4,12) . Each unit on the coordinate plane represents 1 yard. What is the perimeter of the outside of the house?

1 answer

To find the perimeter of the outside of the house, we need to add up the lengths of all four sides of the house.

The length of side AB can be calculated using the distance formula:
AB = sqrt((6-6)^2 + (-6-12)^2)
= sqrt(0^2 + (-18)^2)
= sqrt(0 + 324)
= sqrt(324)
= 18 yards

The length of side BC can also be calculated using the distance formula:
BC = sqrt((6+4)^2 + (-6+6)^2)
= sqrt(16^2 + 0^2)
= sqrt(256)
= 16 yards

The length of side CD can be calculated using the distance formula:
CD = sqrt((-4+4)^2 + (12+6)^2)
= sqrt(0^2 + 18^2)
= sqrt(0 + 324)
= 18 yards

The length of side DA can be calculated using the distance formula:
DA = sqrt((-4-6)^2 + (12+6)^2)
= sqrt(-10^2 + 18^2)
= sqrt(100 + 324)
= sqrt(424)
= 20.6 yards

Therefore, the perimeter of the outside of the house is the sum of all four sides:
Perimeter = AB + BC + CD + DA
= 18 + 16 + 18 + 20.6
≈ 72.6 yards

So, the perimeter of the outside of the house is approximately 72.6 yards.